Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the d The arithmetical hierarchy. Languages and structures.
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There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory ordinal notations, the hyperarithmetical hierarchy and model theory infinitary formulas, consistency properties. Product Details Table of Contents. Table of Contents Preface. The arithmetical hierarchy. Languages and structures.
The hyperarithmetical hierarchy. Infinitary formulas. Computable infinitary formulas. The Barwise-Kreisel Compactness Theorem. Existence of computable structures. Completeness and forcing. The Ash-Nerode Theorem. Computable categoricity and stability. Back-and forth relations. Theorems of Barker and Davey.
Pairs of computable structures. Models of arithmetic. Special classes of structures. Elsevier Science. Studies in Logic and the Foundations of Mathematics Series ,
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Computable Structures and the Hyperarithmetical Hierarchy
The arithmetical hierarchy. Languages and structures. The hyperarithmetical hierarchy. Infinitary formulas. Computable infinitary formulas.